Abstract

Parallel line segments are the basic graphical foundation for geometrical field theories such as General Relativity. Although the concept of parallel and curved lines have been well researched for over a century as a description of gravity, certain controversial issues have persisted, namely point singularities (Black Holes) and the physical interpretation of a scalar multiple of the metric Λ, commonly known as a Cosmological Constant. We introduce a graphical and notational analysis system which we will refer to as Integral Geometry. Through variational analysis of perpendicular line segments we derive equations that ultimately result from the changes in the area bounded by them. Based upon changing area bounded by relative and absolute line segments we attempt to prove the following hypothesis: General Relativity can-not be derived from Integral Geometry. We submit that examination of the notational differences between GR and IG in order to accept the hypothesis could lead to evidence that the inability to merge General Relativity and Quantum Physics may be due to notational and conceptual flaws concerning area inherent in the equations describing them.